A new quasi-steady state hot plate method has been proposed to measure heat flux across a sheet sample such as mould flux film, finally to determine its apparent thermal conductivity via Fourier’s equation. The heat flux across the sheet sample is derived from the volume change caused by melting of ice utilizing a modified Bunsen Ice Calorimeter. This measurement method was applied to Ni-base super alloy (Inconel 600), alumina and PTFE (Teflon) with known thermal conductivity values to confirm the reliability of this new method. The experimental thermal conductivity values obtained were in good agreement with the respective reported values. Measurements were also conducted on sheet silica glasses which sized 20×20×0.5 mm3 and 20×20×1.0 mm3, and produced a value of 1.34 ± 0.03 Wm-1K-1 at 293 K – 303 K under a temperature gradient of 20 Kmm-1, which value is reasonable compared with the reported one. In addition, a process simulation has been applied to confirm the applicability of the present method to mould flux used in continuous casting under a steep temperature gradient at high temperature.